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A306926 A(n, k) is the k-th prime p > 10 where a string of exactly n zeros can be inserted somewhere into the decimal expansion such that the resulting number is also prime; square array, read by antidiagonals, downwards. 1

%I

%S 11,13,19,17,23,17,19,31,19,13,37,41,71,23,13,41,43,73,29,23,23,53,47,

%T 79,37,73,31,17,59,53,97,59,79,43,37,17,61,59,103,71,89,107,53,19,31,

%U 67,67,149,97,179,127,59,47,43,13,71,71,151,103,223,131,61,61

%N A(n, k) is the k-th prime p > 10 where a string of exactly n zeros can be inserted somewhere into the decimal expansion such that the resulting number is also prime; square array, read by antidiagonals, downwards.

%e Array starts as follows:

%e 11, 13, 17, 19, 37, 41, 53, 59, 61, 67, 71, 79, 89, 97

%e 19, 23, 31, 41, 43, 47, 53, 59, 67, 71, 89, 97, 107, 109

%e 17, 19, 71, 73, 79, 97, 103, 149, 151, 157, 173, 181, 223, 229

%e 13, 23, 29, 37, 59, 71, 97, 103, 127, 137, 139, 157, 181, 199

%e 13, 23, 73, 79, 89, 179, 223, 233, 239, 241, 263, 269, 277, 281

%e 23, 31, 43, 107, 127, 131, 137, 139, 149, 151, 163, 173, 179, 181

%e 17, 37, 53, 59, 61, 67, 71, 107, 109, 151, 179, 193, 197, 211

%e 17, 19, 47, 61, 67, 71, 157, 181, 197, 227, 313, 347, 353, 367

%e 31, 43, 103, 113, 127, 137, 149, 157, 163, 173, 191, 241, 257, 277

%e 13, 79, 113, 139, 163, 191, 293, 313, 349, 397, 433, 439, 443, 449

%e 23, 79, 89, 137, 149, 151, 163, 181, 199, 229, 239, 241, 277, 311

%e 41, 79, 131, 157, 167, 197, 199, 227, 229, 233, 241, 347, 349, 359

%e 137, 167, 191, 197, 227, 277, 281, 313, 337, 353, 389, 421, 439, 449

%e Antidiagonals as a triangular array:

%e 11

%e 13, 19

%e 17, 23, 17

%e 19, 31, 19, 13

%e 37, 41, 71, 23, 13

%e 41, 43, 73, 29, 23, 23

%e 53, 47, 79, 37, 73, 31, 17

%e 59, 53, 97, 59, 79, 43, 37, 17

%e 61, 59, 103, 71, 89, 107, 53, 19, 31

%e 67, 67, 149, 97, 179, 127, 59, 47, 43, 13

%e 71, 71, 151, 103, 223, 131, 61, 61, 103, 79, 23

%o (PARI) insert(n, len, pos) = my(d=digits(n), v=[], w=[]); for(y=1, pos, v=concat(v, d[y])); v=concat(v, vector(len)); for(z=pos+1, #d, v=concat(v, d[z])); subst(Pol(v), x, 10)

%o row(n, terms) = my(i=0); if(terms <= 0, print1(""), forprime(p=10, , for(k=1, #digits(p)-1, my(zins=insert(p, n, k)); if(ispseudoprime(zins), print1(p, ", "); i++; break)); if(i>=terms, print(""); break)))

%o array(rows, cols) = for(x=1, rows-1, row(x, cols))

%o array(12, 10) \\ Print initial 12 rows and 10 columns of array

%Y Cf. A215417, A306920. Row 1 is A164329.

%K nonn,tabl,base

%O 1,1

%A _Felix Fröhlich_, Mar 16 2019

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Last modified February 25 21:00 EST 2020. Contains 332258 sequences. (Running on oeis4.)